Finite Group Databasebeta

← #11903821

Subgroups — #11903821

Order 1152.

2629 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
2C3×#5585C212yesmaximal, complemented
3#10595432C212yesmaximal, complemented
4#10595392C212yesmaximal, complemented
5#10594608C214yesmaximal, complemented
6#10594605C212yesmaximal, complemented
7#10594582C212yesmaximal, complemented
8#10594570C214yesmaximal, complemented
9#10594009C212yesmaximal, complemented
10#10594008C211yesmaximal, characteristic
11C4×#3802C212yesmaximal, complemented
12#10593981C214yesmaximal, complemented
13#10593951C212yesmaximal, complemented
14C4×#3797C211yesmaximal, characteristic, complemented
15D3×#559—32nomaximal
16C2×Q8×C3⋊D3C2211yescharacteristic
17C2×#3802C2212yes—
18C2×#3802C2212yes—
19C2×#3802C2212yes—
20C2×C4×D32C2214yes—
21C2×#3797C2211yescharacteristic
22C32×C4×Q8C2211yescharacteristic, complemented
23Q8×C3⋊Dic3C2211yescharacteristic, complemented
24C4⋊C4×C3⋊D3C2211yescharacteristic
25C4⋊C4×C3⋊D3C2212yes—
26#64096C2212yescomplemented
27#64096C2211yescharacteristic, complemented
28C42×C3⋊D3C2211yescharacteristic
29C42×C3⋊D3C2212yes—
30C4×#634C2211yescharacteristic, complemented
31C4×#634C2212yescomplemented
32C3×#947C2214yescomplemented
33C3×#894C2218yescomplemented
34C3×#893C2214yescomplemented
35C3×#875C2214yescomplemented
36C3×#874C2212yes—
37C3×C4×D12C2214yescomplemented
38C3×C4×Dic6C2212yescomplemented
39#63921C2214yes—
40#63921C2214yes—
41#63921C2214yes—
42C4×#627C2212yescomplemented
43#63915C2214yescomplemented
44#63915C2214yescomplemented
45#63914C2212yes—
46#63914C2212yes—
47#63914C2212yes—
48#63913C2218yescomplemented
49#63905C2218yescomplemented
50#63902C2214yescomplemented
51C4×#625C2214yescomplemented
52#63900C2211yescharacteristic
53#63898C2214yescomplemented
54Dic3×D12C2214yescomplemented
55#63891C2218yescomplemented
56#63884C2218yescomplemented
57#63883C2212yes—
58C4×#624C2212yes—
59#63879C2218yescomplemented
60#63863C2214yescomplemented
61#63860C2214yescomplemented
62#63843C2212yescomplemented
63#63838C2212yescomplemented
64C3×#559—32no—
65D3×#127—32no—
66#5713—32no—
67#5681—34no—
68#5681—34no—
69D3×#124—34no—
70D3×#124—34no—
71#5664—38no—
72D3×#123—38no—
73#5585—32no—
74#5585D312yescomplemented
75C4×D3×Q8—32no—
76C4×D3×Q8—32no—
77C4×D3×Q8—61no—
78#5559—34no—
79#5559—34no—
80C4×D3×D4—34no—
81C4×D3×D4—34no—
82C22×D32C2314yes—
83C2×C32×Q8C2311yescharacteristic
84Q8×C3⋊D3—24no—
85C2×C4×C3⋊D3C2312yes—
86C2×C4×C3⋊D3C2311yescharacteristic
87C2×C4×C3⋊D3C2312yes—
88C2×C4×C3⋊D3C2311yescharacteristic
89C2×C4×C3⋊D3C2311yescharacteristic
90C2×#634C2311yescharacteristic
91C2×#634C2312yes—
92C2×C3×D12C2314yes—
93C2×C3×D12C2314yes—
94C2×C3×D12C2314yes—
95C2×C3×C4×D3C2318yes—
96C2×C3×Dic6C2312yes—
97C2×#627C2312yes—
98C2×#625C2314yes—
99C2×#625C2314yes—
100C2×#625C2314yes—
101C2×#624C2312yes—
102C2×#624C2312yes—
103C2×D3×Dic3C2318yes—
104#3802—28no—
105#3802—28no—
106#3802—44no—
107C4×D32—48no—
108#3797—24no—
109C32×C4⋊C4C2311yescharacteristic
110C32×C4⋊C4C2312yes—
111C32×C42C2311yescharacteristic
112C32×C42C2312yes—
113C4⋊(C3⋊Dic3)C2312yes—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750C2312yes—
116#3750C2312yes—
117#3750C2312yes—
118C4×C3⋊Dic3C2311yescharacteristic
119C4×C3⋊Dic3C2312yes—
120C4×C3⋊Dic3C2311yescharacteristic
121C4×C3⋊Dic3C2312yes—
122C4×C3⋊Dic3C2312yes—
123C4×C3⋊Dic3C2311yescharacteristic
124C3×(C2×D3)⋊C4C2318yes—
125C3×(C2×D3)⋊C4C2318yes—
126C3×(C2×D3)⋊C4C2318yes—
127C3×C4⋊Dic3C2312yes—
128C3×Dic3⋊C4C2314yes—
129C3×C4×Dic3C2314yes—
130#3724C2312yes—
131Dic3⋊Dic3C2314yes—
132(C2×D3)⋊Dic3C2318yes—
133(C2×D3)⋊Dic3C2318yes—
134(C2×D3)⋊Dic3C2318yes—
135Dic32C2314yes—
136C2×#559—91noSylow
137C2×D3×Q8—32no—
138C2×D3×Q8—32no—
139C2×D3×Q8—61no—
140C2×D3×D4—34no—
141C2×D3×D4—34no—
142C2×D3×D4—34no—
143C22×C4×D3—38no—
144C3×#127—32no—
145C3×#124—34no—
146C3×#124—34no—
147C3×#123—38no—
148C3×C4×Q8—21no—
149C3×C4×Q8—32no—
150C3×C4×Q8C2×D312yescomplemented
151C3×C4×D4—34no—
152C3×C4×D4—34no—
153#947—34no—
154#947C2×D314yescomplemented
155Q8×Dic3—32no—
156Q8×Dic3—32no—
157Q8×Dic3—61no—
158#940—34no—
159#940—34no—
160#940—34no—
161#936—34no—
162#936—34no—
163#935—38no—
164D4×Dic3—34no—
165D4×Dic3—34no—
166#929—38no—
167C4×#67—38no—
168C4×#67—38no—
169#894—38no—
170#894C2×D318yescomplemented
171#893—34no—
172#893C2×D314yescomplemented
173D3×C4⋊C4—34no—
174D3×C4⋊C4—32no—
175D3×C4⋊C4—32no—
176D3×C4⋊C4—34no—
177D3×C4⋊C4—61no—
178D3×C4⋊C4—62no—
179#887—32no—
180#887—34no—
181#887—32no—
182#887—34no—
183#887—62no—
184#887—61no—
185#886—38no—
186#885—38no—
187#885—38no—
188#885—38no—
189#885—38no—
190#883—38no—
191#883—38no—
192#67⋊C4—38no—
193#67⋊C4—38no—
194D3×C22⋊C4—38no—
195D3×C22⋊C4—38no—
196D3×C22⋊C4—38no—
197#875—34no—
198#875C2×D314yescomplemented
199#874C2×D312yes—
200C4×D12—34no—
201C4×D12C2×D314yescomplemented
202C42×D3—34no—
203C42×D3—32no—
204C42×D3—34no—
205C42×D3—62no—
206C42×D3—61no—
207C4×Dic6—34no—
208C4×Dic6—32no—
209C4×Dic6—34no—
210C4×Dic6—61no—
211C4×Dic6—62no—
212C4×Dic6C2×D312yescomplemented
213C22×C3⋊D3C2411yescharacteristic
214C22×C3×D3C2418yes—
215C2×D32—28no—
216C2×D32—28no—
217C2×D32—28no—
218C32×Q8—22no—
219C2×C32×C4C2411yescharacteristic
220C2×C32×C4C2412yes—
221C2×C32×C4C2412yes—
222C2×C32×C4C2411yescharacteristic
223C2×C32×C4C2411yescharacteristic
224C2×C3⋊Dic3C2412yes—
225C2×C3⋊Dic3C2412yes—
226C2×C3⋊Dic3C2411yescharacteristic
227C2×C3⋊Dic3C2411yescharacteristic
228C2×C3⋊Dic3C2411yescharacteristic
229C4×C3⋊D3—24no—
230C4×C3⋊D3—24no—
231C4×C3⋊D3—22no—
232C4×C3⋊D3#4114yes—
233C4×C3⋊D3#4114yes—
234#634—22no—
235#634—24no—
236C2×C3×Dic3C2414yes—
237C2×C3×Dic3C2414yes—
238C3×D12—28no—
239C3×D12—28no—
240C3×D12—44no—
241C3×C4×D3—48no—
242C3×Dic6—24no—
243#627—24no—
244#625—28no—
245#625—28no—
246#625—44no—
247#624—24no—
248#624—24no—
249D3×Dic3—48no—
250#559—32no—
251#559—92no—
252#559—94no—
253#559—92no—
254#559—94no—
255#559—92no—
256C2×#127—91no—
257C2×#124—92no—
258C2×#124—92no—
259C2×#123—94no—
260C2×C4×Q8—91no—
261C2×C4×Q8—91no—
262C2×C4×D4—92no—
263C2×C4×D4—92no—
264C23×D3—38no—
265C2×C3×Q8—21no—
266C2×C3×Q8—32no—
267C2×C3×Q8C22×D312yes—
268C2×C3×D4—34no—
269C2×C3×D4—34no—
270C2×C3×D4—34no—
271C22×C3×C4—38no—
272C2×#67—38no—
273C2×#67—38no—
274C2×#67—38no—
275C22×Dic3—38no—
276D3×Q8—68no—
277D3×Q8—68no—
278D3×Q8—68no—
279D3×D4—616no—
280D3×D4—616no—
281D3×D4—128no—
282C2×D12C22×D314yes—
283C2×D12C22×D314yes—
284C2×D12C22×D314yes—
285C2×C4×D3—32no—
286C2×C4×D3—32no—
287C2×C4×D3—34no—
288C2×C4×D3—34no—
289C2×C4×D3—32no—
290C2×C4×D3—34no—
291C2×C4×D3—34no—
292C2×C4×D3—38no—
293C2×C4×D3—61no—
294C2×C4×D3—61no—
295C2×C4×D3—62no—
296C2×C4×D3—62no—
297C2×C4×D3—61no—
298C2×C4×D3—1216no—
299C2×C4×D3C22×D318yes—
300C2×Dic6—32no—
301C2×Dic6—34no—
302C2×Dic6—34no—
303C2×Dic6—61no—
304C2×Dic6—62no—
305C2×Dic6C22×D312yes—
306C3×C4⋊C4—21no—
307C3×C4⋊C4—22no—
308C3×C4⋊C4—32no—
309C3×C4⋊C4—34no—
310C3×C4⋊C4C22×D312yes—
311C3×C4⋊C4C22×D314yes—
312C3×C22⋊C4—38no—
313C3×C22⋊C4—38no—
314C3×C22⋊C4—38no—
315C3×C42—22no—
316C3×C42—21no—
317C3×C42—34no—
318C3×C42C22×D312yes—
319C3×C42C22×D314yes—
320#217—38no—
321#217—38no—
322#217—38no—
323(C2×D3)⋊C4—38no—
324(C2×D3)⋊C4—38no—
325(C2×D3)⋊C4—38no—
326(C2×D3)⋊C4C22×D318yes—
327(C2×D3)⋊C4C22×D318yes—
328(C2×D3)⋊C4C22×D318yes—
329C4⋊Dic3—32no—
330C4⋊Dic3—34no—
331C4⋊Dic3—34no—
332C4⋊Dic3—61no—
333C4⋊Dic3—62no—
334C4⋊Dic3C22×D312yes—
335Dic3⋊C4—34no—
336Dic3⋊C4—34no—
337Dic3⋊C4—34no—
338Dic3⋊C4—34no—
339Dic3⋊C4—34no—
340Dic3⋊C4—62no—
341Dic3⋊C4—62no—
342Dic3⋊C4—62no—
343Dic3⋊C4C22×D314yes—
344C4×Dic3—32no—
345C4×Dic3—32no—
346C4×Dic3—34no—
347C4×Dic3—34no—
348C4×Dic3—34no—
349C4×Dic3—32no—
350C4×Dic3—34no—
351C4×Dic3—34no—
352C4×Dic3—62no—
353C4×Dic3—61no—
354C4×Dic3—62no—
355C4×Dic3—61no—
356C4×Dic3—62no—
357C4×Dic3—61no—
358C4×Dic3C22×D314yes—
359C22×C32C2511yescharacteristic
360C2×C3⋊D3C2×#4112yes—
361C2×C3⋊D3C2×#4112yes—
362C2×C3⋊D3H(5,𝔽2)12yes—
363C2×C3×D3—28no—
364C2×C3×D3—28no—
365C2×C3×D3—28no—
366D32—416no—
367C32×C4—22no—
368C32×C4—22no—
369C32×C4—21no—
370C32×C4C2×#4112yes—
371C32×C4C2×#4112yes—
372C3⋊Dic3—22no—
373C3⋊Dic3—22no—
374C3⋊Dic3—21no—
375C3⋊Dic3C2×#4112yes—
376C3⋊Dic3C2×#4112yes—
377C3×Dic3—24no—
378C3×Dic3—24no—
379C22×Q8—91no—
380C22×Q8—91no—
381C22×D4—92no—
382C22×D4—92no—
383C22×D4—92no—
384C23×C4—94no—
385#127—32no—
386#127—92no—
387#127—92no—
388#127—92no—
389#124—34no—
390#124—34no—
391#124—94no—
392#124—98no—
393#124—94no—
394#124—94no—
395#124—94no—
396#123—38no—
397#123—98no—
398#123—98no—
399#123—98no—
400C4×Q8—32no—
401C4×Q8—92no—
402C4×Q8—92no—
403C4×Q8—92no—
404C4×Q8—91no—
405C4×Q8—92no—
406C4×Q8—91no—
407C4×Q8—91no—
408C4×Q8—92no—
409C4×Q8D3211yescharacteristic, complemented
410C4×D4—34no—
411C4×D4—34no—
412C4×D4—94no—
413C4×D4—94no—
414C4×D4—98no—
415C4×D4—94no—
416C4×D4—94no—
417C2×C4⋊C4—91no—
418C2×C4⋊C4—92no—
419C2×C4⋊C4—91no—
420C2×C4⋊C4—92no—
421C2×C22⋊C4—94no—
422C2×C22⋊C4—94no—
423C2×C22⋊C4—94no—
424C2×C42—92no—
425C2×C42—92no—
426C2×C42—91no—
427C23×C3—38no—
428C22×D3—32no—
429C22×D3—61no—
430C22×D3—616no—
431C22×D3—616no—
432C22×D3—616no—
433C22×D3C23×D318yes—
434C3×Q8—24no—
435C3×Q8—24no—
436C3×Q8—64no—
437C3×D4—68no—
438C3×D4—68no—
439C3×D4—124no—
440C2×C3×C4—21no—
441C2×C3×C4—22no—
442C2×C3×C4—21no—
443C2×C3×C4—22no—
444C2×C3×C4—21no—
445C2×C3×C4—34no—
446C2×C3×C4—34no—
447C2×C3×C4—128no—
448C2×C3×C4C23×D312yes—
449C2×C3×C4C23×D314yes—
450C2×C3×C4C23×D314yes—
451C2×C3×C4C23×D312yes—
452C2×C3×C4C23×D312yes—
453#67—616no—
454#67—616no—
455#67—128no—
456C2×Dic3—32no—
457C2×Dic3—32no—
458C2×Dic3—32no—
459C2×Dic3—34no—
460C2×Dic3—34no—
461C2×Dic3—61no—
462C2×Dic3—61no—
463C2×Dic3—62no—
464C2×Dic3—62no—
465C2×Dic3—61no—
466C2×Dic3—128no—
467C2×Dic3C23×D314yes—
468C2×Dic3C23×D314yes—
469D12—28no—
470D12—28no—
471D12—44no—
472C4×D3—38no—
473C4×D3—38no—
474C4×D3—48no—
475C4×D3—64no—
476C4×D3—64no—
477C4×D3—68no—
478C4×D3—68no—
479C4×D3—68no—
480C4×D3—64no—
481C4×D3—68no—
482C4×D3—68no—
483C4×D3—124no—
484C4×D3—122no—
485C4×D3—128no—
486Dic6—24no—
487Dic6—68no—
488Dic6—68no—
489Dic6—68no—
490Dic6—64no—
491Dic6—64no—
492C2×C32C22×#4111yescharacteristic
493C2×C32C22×#4111yescharacteristic
494C2×C32C2×H(5,𝔽2)11yescharacteristic
495C3⋊D3#55914yescomplemented
496C3×D3—48no—
497C24—94no—
498C2×Q8—32no—
499C2×Q8—92no—
500C2×Q8—92no—
501C2×Q8—91no—
502C2×Q8—184no—
503C2×Q8—184no—
504C2×Q8C2×D3211yescharacteristic
505C2×D4—34no—
506C2×D4—34no—
507C2×D4—34no—
508C2×D4—94no—
509C2×D4—94no—
510C2×D4—94no—
511C2×D4—188no—
512C2×D4—188no—
513C2×D4—364no—
514C22×C4—38no—
515C22×C4—92no—
516C22×C4—92no—
517C22×C4—98no—
518C22×C4—91no—
519C22×C4—91no—
520C22×C4—92no—
521C22×C4—92no—
522C22×C4—91no—
523C22×C4—368no—
524C4⋊C4—32no—
525C4⋊C4—34no—
526C4⋊C4—92no—
527C4⋊C4—94no—
528C4⋊C4—92no—
529C4⋊C4—91no—
530C4⋊C4—92no—
531C4⋊C4—92no—
532C4⋊C4—92no—
533C4⋊C4C2×D3211yescharacteristic
534C4⋊C4C2×D3212yes—
535C22⋊C4—38no—
536C22⋊C4—38no—
537C22⋊C4—38no—
538C22⋊C4—98no—
539C22⋊C4—98no—
540C22⋊C4—98no—
541C42—34no—
542C42—94no—
543C42—92no—
544C42—92no—
545C42—92no—
546C42—91no—
547C42—91no—
548C42—91no—
549C42C2×D3212yes—
550C42C2×D3211yescharacteristic
551C22×C3—21no—
552C22×C3—68no—
553C22×C3—68no—
554C22×C3—68no—
555C22×C3C24×D312yes—
556C2×D3—28no—
557C2×D3—28no—
558C2×D3—28no—
559C2×D3—34no—
560C2×D3—34no—
561C2×D3—34no—
562C2×D3—62no—
563C2×D3—62no—
564C2×D3—62no—
565C2×D3—1232no—
566C3×C4—24no—
567C3×C4—24no—
568C3×C4—24no—
569C3×C4—22no—
570C3×C4—22no—
571C3×C4—22no—
572C3×C4—42no—
573C3×C4—41no—
574C3×C4—64no—
575C3×C4—64no—
576C3×C4D3×#4114yes—
577C3×C4D3×#4114yes—
578Dic3—24no—
579Dic3—24no—
580Dic3—34no—
581Dic3—34no—
582Dic3—62no—
583Dic3—62no—
584Dic3—64no—
585Dic3—64no—
586Dic3—64no—
587Dic3—62no—
588Dic3—122no—
589Dic3—121no—
590C32C2×#55911yescharacteristic, complemented, Sylow
591C23—38no—
592C23—91no—
593C23—188no—
594C23—188no—
595C23—188no—
596Q8—22no—
597Q8—64no—
598Q8—184no—
599Q8—184no—
600Q8—182no—
601D4—68no—
602D4—68no—
603D4—124no—
604D4—188no—
605D4—188no—
606D4—364no—
607C2×C4—34no—
608C2×C4—34no—
609C2×C4—91no—
610C2×C4—91no—
611C2×C4—94no—
612C2×C4—94no—
613C2×C4—92no—
614C2×C4—92no—
615C2×C4—91no—
616C2×C4—128no—
617C2×C4—184no—
618C2×C4—182no—
619C2×C4—184no—
620C2×C4—184no—
621C2×C4—184no—
622C2×C4—368no—
623C2×C4C22×D3212yes—
624C2×C4C22×D3212yes—
625C2×C4C22×D3211yescharacteristic
626C2×C4C22×D3211yescharacteristic
627C2×C4C22×D3211yescharacteristic
628C2×C3—21no—
629C2×C3—21no—
630C2×C3—21no—
631C2×C3—128no—
632C2×C3C2×D3×#4112yes—
633C2×C3C2×D3×#4112yes—
634C2×C3D3×H(5,𝔽2)12yes—
635D3—38no—
636D3—48no—
637D3—64no—
638C22—68no—
639C22—68no—
640C22—68no—
641C22—92no—
642C22—92no—
643C22—92no—
644C22—3616no—
645C22C23×D3211yescharacteristic
646C4—22no—
647C4—22no—
648C4—21no—
649C4—64no—
650C4—64no—
651C4—92no—
652C4—92no—
653C4—182no—
654C4—182no—
655C4—181no—
656C4#6430612yes—
657C4#6431912yes—
658C3—21no—
659C3D3×#55912yescomplemented
660C2—94no—
661C2—128no—
662C2C2×#6430611yescharacteristic
663C2C2×#6431911yescharacteristic
664C2#1059669211yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
prime radical#10594008C2
hypercenterC4×Q8D32
hypocenterC32C2×#559
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C4×Q8×C3⋊D3C2semidirect
2. C3×#5585C2semidirect
3. #10595432C2semidirect
4. #10595392C2semidirect
5. #10594608C2semidirect
6. #10594605C2semidirect
7. #10594582C2semidirect
8. #10594570C2semidirect
9. #10594009C2semidirect
11. C4×#3802C2semidirect
12. #10593981C2semidirect
13. #10593951C2semidirect
14. C4×#3797C2semidirect
22. C32×C4×Q8C22semidirect
23. Q8×C3⋊Dic3C22semidirect
26. #64096C22semidirect
27. #64096C22semidirect
30. C4×#634C22semidirect
31. C4×#634C22semidirect
32. C3×#947C22semidirect
33. C3×#894C22semidirect
34. C3×#893C22semidirect
35. C3×#875C22semidirect
37. C3×C4×D12C22semidirect
38. C3×C4×Dic6C22semidirect
42. C4×#627C22semidirect
43. #63915C22semidirect
44. #63915C22semidirect
48. #63913C22semidirect
49. #63905C22semidirect
50. #63902C22semidirect
51. C4×#625C22semidirect
53. #63898C22semidirect
54. Dic3×D12C22semidirect
55. #63891C22semidirect
56. #63884C22semidirect
59. #63879C22semidirect
60. #63863C22semidirect
61. #63860C22semidirect
62. #63843C22semidirect
63. #63838C22semidirect
74. #5585D3semidirect
150. C3×C4×Q8C2×D3semidirect
154. #947C2×D3semidirect
170. #894C2×D3semidirect
172. #893C2×D3semidirect
198. #875C2×D3semidirect
201. C4×D12C2×D3semidirect
212. C4×Dic6C2×D3semidirect
409. C4×Q8D32semidirect
495. C3⋊D3#559semidirect
590. C32C2×#559semidirect
659. C3D3×#559semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C4×Q8×C3⋊D32
C3×#55852
#105954322
#105953922
#105946082
#105946052
#105945822
#105945702
#105940092
#105940082
C4×#38022
#105939812
#105939512
C4×#37972
D3×#5593